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Thus far we have supposed that the farmer is content to get along with his original amount of land and capital, and to increase his product by means of an increased use of labor. Other possibilities are, of course, open to him. It might happen that he would be content to do without additional laborers, using instead an increased equipment of capital. By purchasing more draft animals, more labor-saving machinery, improved fertilizers, or possibly by installing drains or irrigation ditches, as the case may be, he may be able to raise considerably more corn than he could without such investments. But here, again, he will find the possibilities of increasing his product subject to the same limitations that would have prevailed had he increased his labor force. With a team of horses he will be able to accomplish more than he could with one horse; two teams of horses may still further increase the productivity of the farm; a third would probably be of very little advantage, and a fourth team still less useful. So with investments of capital in other forms: the law of diminishing productivity is a remorseless physical fact which the farmer has to reckon with. But the concrete form in which the problem presents itself to him is this: Will a further investment of money in a specific kind of capital goods pay me? Here the farmer has to make on the one hand the best estimate he can of the amount which the proposed capital goods will add to his annual product, and of the probable selling value of the increased product. On the other hand, he has to count his increased annual expenses. These will include (1) the original cost of the additional equipment, divided into annual costs according to its probable durability (each year's costs being properly only the wear and tear, or "depreciation attributable to that year's use); (2) the maintenance or upkeep (including such things as ordinary repairs on machinery and the cost of feeding horses), and (3) the interest on the investment (what the farmer has to pay if he borrows the necessary funds from some one else, or what he might have lent his money for to some one else if he uses his own funds). Guided by these estimates, the farmer will naturally increase his equipment of capital goods so far as the returns from the added product would more than suffice to cover his increased costs. Beyond this point he

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could not wisely go. The last increment of capital - which just suffices to pay for itself is the marginal increment of capital, and the added product attributable to it is the marginal product of capital.

The diagrams portraying the operation of the law of the diminishing productivity of labor will serve as well to illustrate the diminishing productivity of capital. Assuming that the amount of land and the amount of labor to be utilized are definite in quantity, the successive rectangles in Figure 1 represent the increase in the gross product attributable to each of successive increments of capital. Figure 2 represents the same conditions, except that each increment of capital is assumed to be indefinitely small.

If (in Figure 2) BN represents the marginal product of capital, the whole return imputed to capital is, of course, represented by the rectangle OBNÍ. The area above the line HN represents the part of the product which is available for rent and wages, the farmer's profits being derived from any surplus that is left after these demands are satisfied.

There is one difficulty in the foregoing analysis, however, that may have been noted by the reader. What is meant by an "increment of capital"? In the case of labor the "increment of labor" can be interpreted as the labor of one man (for any definite period of time that may be chosen), the one man being assumed (for the purpose of simplicity in the analysis) to be of equal efficiency with all others constituting the labor supply. It is just as practicable, of course, to assume that one horse is, for the farmer's purposes, just as efficient as another horse, that only one kind of plow is available, and that one bushel of fertilizer is exactly like any other bushel of fertilizer; but this does not help us out of our difficulty. For how can we blend horses, plows, and fertilizers into one concept, and divide them into "increments of capital"? One way of getting around the difficulty is to think of the capital which the farmer combines with his labor and his land in terms of its money value. In this sense an increment of capital might be a dollar's worth of capital, or ten dollars' worth of capital, without reference to the different kinds of concrete production goods really composing it. This device is useful for some purposes, but it obscures the fundamental fact that capital gets its value from its ability to secure an income for its owner. The purpose of this analysis of diminishing productivity is to open the way for a discussion of the valuation of the services of land, labor, and capital. To use the term "capital" in the sense of capital value at this stage in the discussion would only lead us into a circular argument. This point cannot be further elaborated here, but should be kept in mind by the reader in connection with the discussion of interest in a subsequent chapter. As a matter of fact the law of diminishing productivity

1 Professor J. B. Clark avoids the difficulty here discussed by using the term "capital" in a sense which corresponds neither to the concrete instruments of production that make up capital goods, nor to the value of these capital goods,

holds for each specific kind of capital that the farmer uses. For example, imagine that the farmer is limited to the use of a fixed amount of all forms of capital except one, - horses, for instance. Then the successive rectangles in Figure I would represent very well the increments of product gained by the use of additional horses, while if the product added by the use of a fifth horse is just about enough to pay for the increased expense, the rectangle DR would represent the marginal product. The illustration can, by a similar process, be made to apply to any other kind of capital. The farmer will normally make use of each specific kind of capital up to the marginal point.

A third way of increasing his product is also open to the farmer. He may think it wiser to get along with his original equipment of capital and his own labor, and to increase his product by utilizing more land. The adoption of this procedure would mean a less intensive cultivation per acre of land. The use of labor and capital would have to be distributed more thinly over the larger acreage. This would result in a smaller product per acre, but the procedure would be warranted if the increase in the annual product should sell for more than the annual cost of the additional acreage. By the annual cost of additional land we mean the rent which the farmer has to pay for the land if he leases it, or the interest on the amount of the purchase price, if he buys it. It is obvious, however, that the combination of more and more land with a fixed amount of labor and capital will result in a smaller and smaller return per acre of land, and that a point will soon be reached beyond which it will not pay the farmer to go. In other words, the law of diminishing productivity rules when land is considered as the variable factor, just as it does when labor or capital is considered as the variable.

The diagrams already used may be adapted to the illustration of the present hypothesis by assuming that equal areas, if successively combined with a given amount of labor and capital, would yield increments of product as represented by the successive rectangles in Figure 1, or by the curve in Figure 2. It is assumed for the sake of simplicity in the illustration that the different acres of land available for the farmer's use are of equal fertility.

but as denoting a self-perpetuating fund which bears the same relation to concrete production goods (including land) that a river does to the drops of water of which it, at a given time, is composed. Professor Clark finds this concept useful in his own analysis (cf. his Distribution of Wealth and Essentials of Economic Theory), but it is altogether too abstract and hypothetical to be of use in the present connection.

The Actual Operation of Diminishing Productivity. It has been assumed thus far that the farmer of our illustration has to be content with a fixed quantity of two of the three factors in production, but that he is at liberty to increase his use of the third factor up to the point where the maximum profits will be gained for himself. Assuming in turn that each of the three factors in production was the variable one, we found that in each case the law was the same maximum profits were obtained when the product added by the last increment of the variable factor would sell for just enough1 to cover the increased expense. In one way, however, this assumption does not correspond with the facts. The farmer is at liberty to increase his products by increasing his utilization, not only of any one, but of any two, or all of the three, factors of production. He may, for example, purchase more draft animals and more machinery, employ more labor, and at the same time acquire more land. To a certain extent the use of one factor may lessen the use of another (as in the case of labor-saving machinery and labor). More often, however, the reverse is true. The acquisition of machinery may necessitate the use of more horses, while the acquisition of more land will often make profitable the use of more labor as well as more capital a fact which is itself implied in the law of diminishing productivity. Although the employment of labor, capital, and land can thus be increased simultaneously, the significance of the law of diminishing productivity is in no wise diminished. The farmer, in deciding upon the purchase of a particular kind of capital good, has to take into account his present and, to some extent, even his probable future supply of other kinds of capital goods, as well as of land and labor, before he can form a judgment as to the amount which the use of the particular capital good will add to his annual product. Moreover, he has to choose between additional investments in labor as against additional investments in land, or additional investments in different kinds of capital. But his effort to get maximum profits will lead him to make those investments

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1 Whether this last unit, which just pays for itself, will be added, is, of course, a matter of indifference. The margin is consequently sometimes called the "margin of indifference."

which promise to result in the greatest additions to his product. The result of this will be, normally, that each factor in production will be utilized up to the marginal point - the point where further utilization would add a product so small as to sell for less than the increased expenses.

Why the farmer should not increase his product indefinitely by increasing his use of all three of the factors in production is a question which does not concern us in this connection. The law of diminishing productivity relates only to the proportions in which land, labor, and different forms of capital are combined. The question of the most profitable size of farm is quite another thing.1

It is not only in agriculture that the law of diminishing productivity is the fundamental thing in determining the proportions in which the factors of production are combined. Every manufacturer has the option of using either relatively more machinery and relatively less labor, or relatively less machinery and relatively more labor in order to produce a certain quantity of goods. He may have to decide, also, between building a six-story factory covering an acre of ground, and a one-story factory covering six acres of ground a problem which is paralleled by the farmer's problem of deciding between the cultivation of a relatively large acreage and the more intensive cultivation of a smaller acreage. The entrepreneur in every kind of undertaking has to decide as to the advisability of a particular investment in land, capital, or labor, with reference to the fundamental question, "Will it pay?" And the profitableness of any such investment is always a matter of the cost of the unit of land, labor, or capital, as compared with the selling value of the quantity which it will add to the entrepreneur's total product.

1 The limitations to the profitable size of a farm or other business unit arise from the fact that the managerial efficiency of the entrepreneur is itself subject to the law of diminishing productivity. Under competition there is a constant tendency for labor, capital, and land to get into the hands of those entrepreneurs who can use them most efficiently, that is, who can pay most for them because they can get the largest product from them. But even if A is a better entrepreneur than B, it may easily happen that B can get a larger product from additional units of labor, capital, and land than A can, if B's existing equipment is considerably smaller than A's. A given farmer cannot extend his use of land, labor, and capital indefinitely, simply because, after his establishment reaches a certain size, other

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